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Multigrid method for the solution of thermal elastohydrodynamic lubrication point contact problem with surface asperities

Vishwanath B. Awati, Parashuram M. Obannavar, Mahesh Kumar Nanjaiah

Abstract

The paper presents, the numerical investigation of point contact thermal elasto-hydrodynamic lubrication (EHL) with surface asperities are analyzed. The effect of temperature and surface roughness on fluid film thickness is studied in detail. The governing equations comprises Reynolds, film thickness, load balance and energy equations with appropriate boundary conditions. The second order finite difference approximation is used to discretize the governing equations and the resultant nonlinear system of algebraic equations is solved using Multigrid V-cycle with full approximation scheme (FAS) technique. Multi level multi integration (MLMI) technique is employed to solve the film thickness equation. The obtained results are illustrated in the form of graphs and tables which are comparable with earlier findings. The film thickness profiles shows dimple near to the outlet region due to temperature-viscosity wedge mechanism. Isothermal minimum film thickness is higher than the thermal minimum film thickness. Minimum film thickness is much smaller due to slide to roll ratio is positive ascompared to negative, whereas the behavior of central film thickness is contrast as that of minimum film thickness.


Keywords

thermal; EHL; multigrid method; FAS; slide to roll ratio; MLMI

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References

1. Crook AW. The lubrication of rollers III. A theoretical discussion of friction and the temperatures in the oil film. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences 1961; 254(1040): 237–258.doi: 10.1098/rsta.1961.0016

2. Sternlicht B, Lewis P, Flynn P. Theory of lubrication and failure of rolling contacts. Journal of Basic Engineering 1961; 83(2): 213–222. doi: 10.1115/1.3658927

3. Cheng HS, Sternlicht B. A numerical solution for the pressure, temperature, and film thickness between two infinitely long, lubricated rolling and sliding cylinders, under heavy loads. Journal of Basic Engineering 1965; 87(3): 695–704.doi: 10.1115/1.3650647

4. DowsonD, Whitaker AV. Paper 4: A numerical procedure for the solution of the elastohydrodynamic problem of rolling and sliding contacts lubricated by a Newtonian fluid. Proceedings of the Institution of Mechanical Engineers 1965; 180(2): 57–71.doi: 10.1243/PIME_CONF_1965_180_064_0

5. Murch LE, Wilson WRD. A thermal elastohydrodynamic inlet zone analysis. Journal of Lubrication Technology 1975; 97(2): 212–216. doi: 10.1115/1.3452559

6. BruggemannH, Kollmann FG. A numerical solution of the thermal elastohydrodynamic lubrication in an elliptical contact. Journal of Lubrication Technology 1982; 104(3): 392–400. doi: 10.1115/1.3253231

7. Kim KH, Sadeghi F. Three-dimensional temperature distribution in EHD lubrication: Part I—Circular contact. Journal of Tribology 1992; 114(1): 32–41. doi: 10.1115/1.2920864

8. Kim KH, Sadeghi F. Three-dimensional temperature distribution in EHD lubrication: Part II—Point contact and numerical formulation. Journal of Tribology 1993; 115(1): 36–45. doi: 10.1115/1.2920984

9. Salehizadeh H, Saka N. Thermal non-Newtonian elastohydrodynamic lubrication of rolling line contacts. Journal of Tribology 1991; 113(3): 481–491.doi: 10.1115/1.2920649

10. Wolff R, Kubo A. The application of Newton-Raphsonmethod to thermal elastohydrodynamic lubrication of line contacts. Journal of Tribology 1994; 116(4): 733–740.doi: 10.1115/1.2927327

11. Kazama T, Ehret P, Taylor CM. On the effects of the temperature profile approximation in thermal Newtonian solutions of elastohydrodynamic lubrication line contacts. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 2001; 215(1): 109–120.doi: 10.1243/1350650011541666

12. Lee RT, Hsu CH, KuoWF. Multilevel solution for thermal elastohydrodynamic lubrication of rolling/sliding circular contacts. Tribology International 1995; 28(8): 541–552. doi: 10.1016/0301-679X(96)85542-3

13. Ehret P, DowsonD, Taylor CM. Thermal effects in elliptical contacts with spin conditions. Tribology Series 1999; 36: 685–703. doi: 10.1016/S0167-8922(99)80088-1

14. Qu S, Yang P, Guo F. Theoretical investigation on the dimple occurrence in the thermal EHL of simple sliding steel-glass circular contacts. Tribology International 2000; 33(1): 59–65.doi: 10.1016/S0301-679X(00)00031-1

15. Yang P, Qu S,Kaneta M, Nishikawa H. Formation of steady dimples in point TEHL contacts. Journal of Tribology 2001; 123(1): 42–49.doi: 10.1115/1.1332399

16. Guo F, Yang P, Qu S. On the theory of thermal elastohydrodynamic lubrication at high slide-roll ratios—Circular glass-steel contact solution at opposite sliding. Journal of Tribology 2001; 123(4): 816–821. doi: 10.1115/1.1330739

17. Kim HJ, Ehret P, Dowson D, Taylor CM. Thermal elastohydrodynamic analysis of circular contacts part 1: Newtonian model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 2001; 215(4): 339–352.doi: 10.1243/1350650011543583

18. Kim HJ, Ehret P, Dowson D, Taylor CM. Thermal elastohydrodynamic analysis of circular contacts part 2: Non-Newtonian model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 2001; 215(4): 353–362. doi: 10.1243/1350650011543592

19. CannPM,Spikes HA. Determination of the shear stress of lubricants in elastohydrodynamic contacts. Tribology Transactions 1989; 32(3): 414–422. doi: 10.1080/10402008908981908

20. Liu X, Jiang M, Yang P, Kaneta M. Non-Newtonian thermal analyses of point EHL contacts using the Eyring model. Journal of Tribology 2005; 127(1): 70–81. doi: 10.1115/1.1843161

21. Greenwood JA, Williamson JBP. Contact of nominally flat surfaces. Proceedings of the Royal Society of London (A). Mathematical and Physical Sciences 1966; 295(1442): 300–319. doi: 10.1098/rspa.1966.0242

22. Greenwood JA, Tripp JH. The contact of two nominally flat rough surfaces. Proceedings of the Institution of Mechanical Engineers 1970; 185(1): 625–633.doi: 10.1243/PIME_PROC_1970_185_069_02

23. Patir N, Cheng HS. An average flow model for determining effects of three-dimensional roughness on partial hydrodynamic lubrication. Journal of Lubrication Technology 1978; 100(1): 12–17. doi: 10.1115/1.3453103

24. Sadeghi, F, SuiPC. Thermal elastohydrodynamic lubrication of rough surfaces. Journal of Tribology 1990; 112(2): 341–346. doi: 10.1115/1.2920262

25. Chang L. A deterministic model for line-contact partial elastohydrodynamic lubrication. Tribology International 1995; 28(2): 75–84.doi: 10.1016/0301-679X(95)92697-4

26. Hu YZ,Zhu D. A full numerical solution to the mixed lubrication in point contacts. Journal of Tribology 2000; 122(1): 1–9. doi: 10.1115/1.555322

27. Wang QJ, Zhu D, Cheng HS, et al. Mixed lubrication analyses by a macro-micro approach and a full-scale mixed EHL model. Journal of Tribology 2004; 126(1): 81–91. doi: 10.1115/1.1631017

28. Lu X, Khonsari MM, Gelinck ERM. The stribeck curve: Experimental results and theoretical prediction. Journal of Tribology 2006; 128(4): 789–794. doi: 10.1115/1.2345406

29. Deolalikar N, Sadeghi F, Marble S. Numerical modeling of mixed lubrication and flash temperature in EHL elliptical contacts. Journal of Tribology 2008; 130(1): 011004. doi: 10.1115/1.2805429

30. Yang P, Cui J, Jin ZM, DowsonD. Influence of two-sided surface waviness on the EHL behavior of rolling/sliding point contacts under thermal and non-Newtonian conditions. Journal of Tribology 2008; 130(4): 041502. doi: 10.1115/1.2958078

31. Akbarzadeh S, Khonsari MM. Performance of spur gears considering surface roughness and shear thinning lubricant. Journal of Tribology 2008; 130(2): 021503. doi: 10.1115/1.2805431

32. Sojoudi H, Khonsari MM. On the behavior of friction in lubricated point contact with provision for surface roughness. Journal of Tribology 2010; 132(1): 012102. doi: 10.1115/1.4000306

33. Zhu D, Wang QJ. Effect of roughness orientation on the elastohydrodynamic lubrication film thickness. Journal of Tribology 2013; 135(3): 031501.doi: 10.1115/1.4023250

34. Masjedi M, Khonsari MM. On the effect of surface roughness in point-contact EHL: Formulas for film thickness and asperity load. Tribology International 2015; 82(A): 228–244. doi: 10.1016/j.triboint.2014.09.010

35. Awati VB, Naik S, Kumar M.Multigrid method for the solution of EHL point contact with bio-based oil as lubricants for smooth and rough asperity. Industrial Lubrication and Tribology 2018; 70(4): 599–611.doi: 10.1108/ILT-12-2016-0314

36. Zhang B, Wang J, Omasta M, Kaneta M. Variation of surface dimple in point contact thermal EHL under ZEV condition. Tribology International 2016; 94: 383–394.doi: 10.1016/j.triboint.2015.09.036

37. Cui J, Yang P, Kaneta M, Krupka I. Numerical study on the interaction of transversely oriented ridges in thermal elastohydrodynamic lubrication point contacts using the Eyring shear-thinning model. Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 2017; 231(1): 93–106.doi: 10.1177/1350650116646943

38. Awati VB, Kumar NM, Bujurke NM. Numerical solution of thermal EHL line contact with bio-based oil as lubricant. Australian Journal of Mechanical Engineering 2022; 20(1): 231–244.doi: 10.1080/14484846.2019.1699720

39. Liu X, Cui J, Yang P. Size effect on the behavior of thermal elastohydrodynamic lubrication of roller pairs. Journal of Tribology 2012; 134(1): 011502. doi: 10.1115/1.4005515

40. Hultqvist T, Vrcek A, Marklund P, et al. Transient analysis of surface roughness features in thermal elastohydrodynamic contacts. Tribology International 2019; 141: 10595.doi: 10.1016/j.triboint.2019.105915

41. Zhao Y, Wong PL, Mao JH. Solving coupled boundary slip and heat transfer EHL problem under large slide-roll ratio conditions. Tribology International 2019; 133: 73–87.doi: 10.1016/j.triboint.2019.01.013

42. Zhang M, Wang J, Yang P, et al. A thermal EHL investigation for size effect of finite line contact on bush-pin hinge pairs in industrial chains. Industrial Lubrication and Tribology 2019; 72(5): 695–701.doi: 10.1108/ILT-10-2019-0448

43. Zhang M, Wang J, Cui J, Yang P. A thermal investigation on plate-pin hinge pairs in silent chains using a narrow finite line contact. Industrial Lubrication and Tribology 2020; 72(10): 1139–1145. doi: 10.1108/ILT-11-2019-0498

44. Zhao Y, Wong PL. Thermal-EHL analysis of slip/no-slip contact at high slide-to-roll ratio. Tribology International 2021; 153: 106617. doi: 10.1016/j.triboint.2020.106617

45. Brandt A. Multi-level adaptive solutions to boundary-value problems. Mathematics of Computation 1977; 31(138): 333–390.

46. Lubrecht AA, ten Napel WE, Bosma R.Multigrid, an alternative method of solution for two-dimensional elastohydrodynamically lubricated point contact calculations. Journal of Tribology 1987; 109(3): 437–443.doi: 10.1115/1.3261467

47. Venner C. Multilevel Solution of the EHL Line and Point Contact Problems [PhD thesis]. University of Twente; 1991.

48. Roelands CJA, Winer WO, Wright WA. Correlational aspects of the viscosity-temperature-pressure relationship of lubricating oils.(Dr In dissertation at Technical University of Delft, 1966). Journal of Lubrication Technology 1971; 93(1): 209–210.doi: 10.1115/1.3451519

49. Dowson D, Higginson GR. Elasto-Hydrodynamic Lubrication: The Fundamentals of Roller Gear Lubrication. Pergamon Press; 1966.

50. Pai SI. Viscous Flow Theory, Vol. 1 (One): Laminar Flow. D. Van Nostrand Company; 1956.

51. Liu J. Thermal Non-Newtonian Elastohydrodynamic Lubrication of Point Contacts [PhD thesis]. The University of Leeds; 1994.

52. Venner CH, Lubrecht AA. Multi-Level Methods in Lubrication. Elsevier; 2000.

53. Hamrock BJ, Dowson D. Isothermal elastohydrodynamic lubrication of point contacts: Part 3—Fullyflooded results. Journal of Lubrication Technology 1977; 99(2): 264–275. doi: 10.1115/1.3453074

54. Ehret P, Dowson D, Taylor CM, Wang D. Analysis of isothermal elastohydrodynamic point contacts lubricated by


DOI: https://doi.org/10.59400/mea.v1i1.94
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